1.

Two identical very small metal spheres, A and B, that are electrically neutral are fixed at a distance R On insulating handles. A third identical sphere C carrying charge Q is also connected to an insulating handle. C ia first brought into contact with A and B and then moved away from these two spheres. It is found that A and B apply F_1 force on each other. Now C with the remaining charge is again brought into contact with A and then moved away from A and B. It is found that A and B apply F_2 force on each other. Now C is further brought into contact with B and then moved away from A and B. It is found that A and B apply F_3 force on each other Finally B is moved closer to A at a distance r, such that the force between them again becomes F_1. The magnitude of F_1//F_2 is

Answer»

`3//4`
`4//3`
`4//5`
`5//4`

Solution :Charge acquired by A when C touches it for the first time , `q_1=Q//2`
Charge acquired by B and C touches it for the first time, `q_2=Q//4`
FORCE between A and B :`F_1=1/(4piepsilon_0) ((Q/2)(Q/2))/R^2 =1/8 1/(4piepsilon_0) Q^2/R^2`…(i)
Charge acquired by A when C touches if for the second time ,
`q_3=1/2 (Q/2+Q/4)=(3Q)/8`
Force between A and B : `F_2=1/(4piepsilon_0) (("3Q"/8)(Q/4))/R^2 =3/32 1/(4piepsilon_0) Q^2/R^2`...(II)
`F_1/F_2=1/8xx32/3=4/3`


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